My friend at the juggling club does something that is similar, but not exactly the same. He has a one-cup diabolo (a monobolo?) that he wraps with a rope, and throws like a top, to spin on the floor. It spins quite well!
Then he drops the top part of an old Duncan Twin Spin top into the spinning monobolo cup. The Twin Spin half chatters around and around in the cup for a bit, being spun as it does so, and then flies out and onto the floor....where it spins on its own tip. Very cool to watch!
I can't remember whether he drops the top in upside down, or right side up....but I know it makes a difference....